piazzesi swanson(jme2008)

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Futures prices as risk-adjusted forecasts of monetary policy$

Monika Piazzesi a,, Eric T. Swanson b

a University of Chicago, NBER, Chicago, USAb Federal Reserve Bank of San Francisco, USA

a r t i c l e i n f o

Article history:Received 7 August 2006

Received in revised form

4 April 2008

Accepted 4 April 2008Available online 2 May 2008

Keywords:

Federal funds futures

Monetary policy

Risk premia

a b s t r a c t

Many researchers have used federal funds futures rates as measures of financial marketsexpectations of future monetary policy. However, to the extent that federal funds futures

reflect risk premia, these measures require some adjustment. In this paper, we document

that excess returns on federal funds futures have been positive on average and strongly

countercyclical. In particular, excess returns are surprisingly well predicted by macro-

economic indicators such as employment growth and financial business-cycle indicators

such as Treasury yield spreads and corporate bond spreads. Excess returns on eurodollar

futures display similar patterns. We document that simply ignoring these risk premia

significantly biases forecasts of the future path of monetary policy. We also show that risk

premia matter for some futures-based measures of monetary policy shocks used in the

literature.

& 2008 Elsevier B.V. All rights reserved.

1. Introduction

Predicting the future course of monetary policy is of tremendous importance to financial market participants. The

current state of the art in this area is to use futures contracts on the short-term interest rate that is targeted by the central

bank and to interpret the futures rate on, say, the December federal funds futures contract as the market expectation of

what the federal funds rate will be in December. This procedure is widely used in the financial press (e.g., The Wall Street

Journal, 2005; Financial Times, 2005), by Fed watchers (e.g., Altig, 2005; Hamilton, 2006), by central banks (e.g., European

Central Bank Monthly Bulletin, 2005, p. 24; Federal Reserve Monetary Policy Report to Congress, 2005, p. 22), and in the

academic literature (e.g., Krueger and Kuttner, 1996; Rudebusch, 1998, 2002; Bernanke and Kuttner, 2005 ).1

The standard practice is appealing for many reasons. First, producing the forecasts is simplethe rates on various

contracts can be obtained directly from futures exchanges at any time during the day. Second, the forecasts work

wellfederal funds futures outperform forecasts based on alternative methods, such as sophisticated time series

specifications, monetary policy rules, and forecasts derived from Treasury bills or other financial market instruments

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jme

Journal of Monetary Economics

0304-3932/$- see front matter & 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.jmoneco.2008.04.003

$We are particularly indebted to Charlie Evans and Frank Schorfheide (our discussants at the Stanford/FRBSF conference), and Donald Kohn for helpful

suggestions. We thank Claire Hausman for excellent research assistance, and John Cochrane, Lou Crandall, Darrell Duffie, Bob Hall, David Laibson, Andy

Levin, Brian Sack, Martin Schneider, Jiang Wang, Jonathan Wright, and seminar participants at the Bundesbank, European Central Bank, Federal Reserve

Board, Universities at Columbia, Heidelberg, Mannheim, Stanford, Rochester, Harvard, and the Wharton School, the IMA Workshop at the University of

Minnesota, the NBER Summer Institute, and the Society of Economic Dynamics Meetings for comments. The views expressed in this paper, and any errors

and omissions, are those of the authors, and are not necessarily those of the individuals listed above, the management of the Federal Reserve Bank of San

Francisco, or any other individual within the Federal Reserve System. Corresponding author.

E-mail address: [email protected] (M. Piazzesi).1 Some of these studies allow for constant risk premia.

Journal of Monetary Economics 55 (2008) 677 691
http://www.sciencedirect.com/science/journal/monechttp://www.elsevier.com/locate/jmehttp://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.jmoneco.2008.04.003mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.jmoneco.2008.04.003http://www.elsevier.com/locate/jmehttp://www.sciencedirect.com/science/journal/monec


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(e.g., Evans, 1998; Gurkaynak et al., 2007). Third, previous studies did not find any large time variation in risk premia in fed

funds futures (e.g., Krueger and Kuttner, 1996; Sack, 2004; Durham, 2003).2

However, there is by now a large and well-accepted body of evidence in the finance literature against the expectations

hypothesis for Treasury yields (e.g., Fama and Bliss, 1987; Stambaugh, 1988; Campbell and Shiller, 1991; Cochrane and

Piazzesi, 2005). Over a very wide range of sample periods and bond maturities, excess returns on Treasury securities have

been positive on average, time-varying, and significantly predictable. Time-varying risk premia in these markets may well

carry over to related markets and therefore lead to systematic deviations of fed funds futures rates from expectations of the

subsequently realized fed funds rate.In this paper, we show that the expectations hypothesis also fails for federal funds futures. In particular, excess returns

on fed funds futures contracts at even short horizons have been positive on average and significantly predictable. The R2s

depend on the forecast horizon and range from 10% at a two-month horizon up to 39% at a six-month horizon. We find that

macroeconomic business-cycle indicators such as employment growth capture this predictability surprisingly well. We

also find that financial business-cycle indicators such as corporate bond spreads and Treasury yield spreads do well at

predicting excess returns. These findings stand up to a battery of robustness checks, including bootstrapped test statistics,

real-time data, subsample stability pre- and post-1994, rolling-endpoint regressions, out-of-sample forecasts, and a

comparison to excess returns on eurodollar futures, for which we have a somewhat longer sample.

We exploit the significant predictability of excess returns on futures to propose a risk adjustment to forecasts of

monetary policy. We find that not implementing our risk adjustment can produce very misleading results. Specifically,

forecasts based on the expectations hypothesis make large mean errors and large mean-squared errors. Moreover, errors

from unadjusted forecasts vary systematically over the business cycle; futures rates tend to overpredict in recessions and

underpredict in booms. Non-risk-adjusted forecasts also tend to perform very poorly around economic turning points,adapting too slowly to changes in the direction of monetary policy. For example, right before recessions, when the Fed has

already started easing, fed funds futures keep forecasting high funds rates. As a consequence, forecast errors using

unadjusted futures rates are more highly autocorrelated than are forecast errors using our risk-adjusted futures rates.

Our findings also suggest that monetary policy shocks may not be accurately measured by the difference between the

fed funds rate target and an ex ante market expectation based on fed funds futures. Indeed, we document that the amount

by which we need to adjust these shocks can be substantial, at least relative to the size of the shocks themselves. However,

risk premia seem to change primarily at business-cycle frequencies, which suggests that we may be able to difference

them out by looking at one-day changes in near-dated fed funds futures on the day of a monetary policy announcement.

Indeed, our results confirm that differencing improves these policy measures.

Our findings for federal funds futures complement those in the traditional finance literature on Treasuries in several

ways. First, we find that the most important predictive variables for excess returns are macroeconomic variables, such as

employment growth. This finding allows us to link the predictability in excess returns directly to the business cycle, while

the existing literature on Treasuries has focused mainly on predictability using financial variables such as term spreads(e.g., Cochrane and Piazzesi, 2005).

Second, fed funds futures are actually traded securities, while the zero-coupon yield data used in Fama and Bliss (1987)

and many other papers are data constructed by interpolation schemes. While the predictability patterns in this artificial

data may not lead to profitable trading rules based on actual securities, investors can implement our results directly by

trading in fed funds futures. Interestingly, we document evidence that suggests that futures market participants were

aware of these excess returns in real time: traders that are classified as not hedging by the U.S. Commodity Futures

Trading Commission (CFTC) went long in these contracts precisely when we estimate that expected excess returns on these

contracts were high, and they went short precisely in times when we estimate expected excess returns were very low.

Finally, fed funds futures contracts have maturities of just a few months and may therefore be less risky than Treasury

notes and bonds, which have durations of several years; moreover, the holding periods relevant for measuring excess

returns on fed funds futures are less than one year, while the results for Treasuries typically assume that the investor holds

the securities for an entire year (an exception is Stambaugh, 1988, who studies Treasury bills). Given the short maturities

and required holding periods to realize excess returns in the fed funds futures market, one might think that risk premia inthis market would be very small or nonexistent. We find that this is not the case.

Throughout this paper, we will often use the label risk premia to refer to predictable returns in excess of the risk-free

rate. This use of language should not be interpreted as taking a particular stance on the structural interpretation of our

results. The existing literature has proposed several appealing explanations for why excess returns on these contracts might

be predictable. Some of these explanations are based on preferences: for example, investors may exhibit risk aversion

which varies over the business cycle, or care about the slow-moving, cyclical consumption of items like housing. Other

explanations are based on beliefs that deviate from rational expectations, for example because of learning or for

psychological reasons. It is not easy to make the case for just one of these explanations: beliefs and other preference

2 These studies run regressions of one-month excess returns on fed funds futures on a variety of variables, including macroeconomic variables. While

some of the regression coefficients are statistically significant, they are economically small. Our results are different: we show that for holding periodslonger than one month, risk premia are large on average and vary over time substantially.

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parameters can often not be identified separately. We therefore set aside these issues as beyond the scope of the present

paper.

The remainder of the paper proceeds as follows. Section 2 shows that measures of excess returns on fed funds futures

are identical to monetary-policy forecast errors and can be predicted using business-cycle indicators such as employment

growth or corporate bond spreads. Section 3 performs a battery of robustness checks. Section 4 presents our risk-

adjustment to policy forecasts and shows that failing to implement the adjustment can lead to substantial mistakes, so that

the predictability of excess returns is economically as well as statistically significant. Section 5 investigates the implications

of our results for measures of monetary policy shocks used in the literature. Section 6 concludes.

2. Excess returns on federal funds futures

Federal funds futures contracts have traded on the Chicago Board of Trade exchange since October 1988 and settle based

on the average federal funds rate that prevails over a given calendar month.3 Let fnt denote the fed funds futures contract

rate for month t n as quoted at the end of month t. We will refer to n 1 as the one-month-ahead futures contract, n 2

as the two-month-ahead contract, and so on. Let rtn denote the ex post realized value of the federal funds rate for month

t n, calculated as the average of the daily fed funds rates in month t n for comparability to the fed funds futures

contracts.

The buyer of a fed funds futures contract locks in the contracted rate fnt for the contract month t n on a $5 million

deposit (the $5 million deposit is never actually made by the buyer; this is only the number that is used to compute the

payoff of the contract at maturity). The contracts are cash-settled the day after expiration, with expiration occurring at the

end of the contract month. At that time, the buyer receives $5 million times the difference between fnt and the realized fed

funds rate rtn converted to a monthly rate.4 As is standard for futures contracts, there are no up-front costs to either party

of entering into the contract; both parties simply commit to the contract rate at time t and receive their payoffs at time

t n.

For the buyer of the futures contract, the amount fnt rtn $5 million represents the payoff of a zero-cost portfolio.

Using common terminology (e.g., Cochrane, 2001, p. 11), we refer to this difference, fnt rtn, as an excess return. We

denote the excess return for the buyer of the contract by

rxntn f

nt rtn. (1)

Since we will consider futures contracts with maturities n ranging from one to six months, the excess returns in (1) will

correspond to different holding periods for different values of n. To make excess returns on these different contracts more

directly comparable, we also report statistics for annualized excess returns, which are computed by multiplying the excess

returns in (1) by 12=n. Also, we measure returns in basis points. These conventions will apply throughout the paper.

Eq. (1) treats fed funds futures contracts as forward contracts, and thereby abstracts from the fact that futures contractsare marked to market every day, based on collateral posted in interest-bearing accounts. The appendix of the working

paper version of this article (Piazzesi and Swanson, 2006) explains this procedure in more detail, computes excess returns

on fed funds futures contracts taking into account the effects of marking to market, and shows that the difference between

a precise definition of excess returns on futures contracts and the simplification in Eq. (1) is very small and does not matter

for our results below. We therefore use (1) as the definition of excess returns in this paper for simplicity.

The simplification in Eq. (1) also has the advantage that excess returns are easily linked to forecasting. Under the

expectations hypothesis, futures are expected future short rates: fnt Etrtn. Thus, Eq. (1) not only represents excess

returns, but also minus the forecast error under the expectations hypothesis. This coincidence makes it easy to see how we

can adjust futures-based forecasts for risk premia.

2.1. Average excess returns

To investigate whether average excess returns on federal funds futures contracts are zero, we run the regression:

rxntn a

n ntn (2)

for different contract horizons n.

Panel A in Table 1 presents results from regression (2) for the forecast horizons n 1; . . . ; 6 months over the entire

period for which we have fed funds futures data, October 1988 through December 2005. This period will be the baseline for

all of our regressions below. We run the regression at monthly frequency, sampling the futures data on the last day of each

month t.5 We compute standard errors using the heteroskedasticity- and autocorrelation-consistent procedure from

3 The average federal funds rate is calculated as the simple mean of the daily averages published by the Federal Reserve Bank of New York, and the

federal funds rate on a non-business day is defined to be the rate that prevailed on the preceding business day.4 This means that f

nt rtn gets multiplied by

112 according to the quoting convention in the fed funds futures market, which uses a 30-day month and

360-day year. See the CBOT web site for additional details.

5 We restrict attention to monthly data in order to avoid variations in the maturity of the contracts that would arise over the course of each month:for example, with daily data, the one-month-ahead contract could have as few as 28 and as many as 61 days until maturity, which is a significant variation

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Hodrick (1992), which generalizes the Hansen and Hodrick (1988) procedure for overlapping contracts to the case of

heteroskedasticity, allowing for n 1 lags of excess returns to be serially correlated due to contract overlap. Throughout

this paper, we report HAC t-statistics based on these standard errors. Finally, to help account for the small-sample

distributional properties of these t-statistics, Table 1 reports the bootstrapped p-value for each t-statistic using 50,000

bootstrap draws following Horowitz (2004).6

As can be seen in Panel A, average excess returns on fed funds futures have been significantly positive over our

sample, ranging from about 3 to 5 basis points per month (3561 bp per year). For example, buying the six-month-ahead

futures contract and holding it to maturity is a strategy that generated a return of 61.4bp per year on average.7

Longer-horizon contracts have had greater excess returns on average even on a per-month or per-year basis.

Table 1

Unconditional and conditional expected excess returns

n 1 2 3 4 5 6

Panel A: average excess returns

an , unannualized 2.9 6.3 10.5 16.1 23.2 30.7

an , annualized 35.0 38.1 42.2 48.3 55.6 61.4

(t-Stat) (3.7) (3.4) (3.0) (2.9) (2.9) (2.7)

[Bootstrap p-value] [0.001] [0.001] [0.007] [0.016] [0.022] [0.037]

Panel B: recession dummy

Constant 28.2 26.6 28.8 33.3 40.0 49.4

(t-Stat) (3.3) (2.8) (2.3) (2.3) (2.3) (2.4)


Recession dummy 77.8 131.3 151.2 169.3 177.0 168.6

(t-Stat) (1.4) (2.1) (3.1) (5.1) (6.6) (4.7)


R2 0.03 0.10 0.14 0.16 0.17 0.13

Panel C: nonfarm payrolls

Constant 0.3 1.7 6.6 16.8 31.3 45.7

fn

t0.13 0.19 0.25 0.32 0.38 0.44

(t-Stat) (2.1) (2.4) (3.1) (4.5) (7.0) (10.9)[Bootstrap p-value] [0.078] [0.017] [0.003] [0.001] [0.000] [0.000]

DNFPt1 0.20 0.37 0.51 0.62 0.70 0.73

(t-Stat) (1.8) (3.0) (3.8) (5.1) (7.2) (11.1)


R2 0.03 0.10 0.18 0.25 0.32 0.39

Panel D: corporate bond spread

Constant 43.7 67.6 89.1 105.4 125.3 142.7

fn

t0.06 0.06 0.08 0.10 0.14 0.18

(t-Stat) (1.3) (1.0) (1.4) (2.1) (2.6) (3.0)


BBB spread 0.34 0.52 0.62 0.69 0.75 0.80

(t-Stat) (1.8) (2.6) (2.9) (2.9) (3.0) (2.8)


R2

0.03 0.08 0.12 0.16 0.20 0.22

Note: n denotes the horizon of the fed funds futures contract in months. The sample for each regression is 1988:102005:12 at monthly frequency,

sampled on the last day of each month. Excess returns are measured in annualized basis points, except for Panel A, which reports both unannualized and

annualized results. HAC t-statistics are reported in parentheses, and bootstrapped p-values for the t-statistics are in brackets; t-statistics for constants in

Panels CD not reported. See text for details.

(footnote continued)

in the holding period required to realize the excess return on the contract. In turn, these differences in maturities and holding periods influence the size

and time variation of risk premia, as we will show below. Also, these variations would translate into different forecasting horizons when we later use our

results to forecast the fed funds rate. Nonetheless, our results are all similar when we sample the data at daily rather than monthly frequency.6 Following Horowitz (2004), observations are resampled from the data with replacement to generate 50,000 synthetic samples of the same size as

the original. To account for possible serial dependence of the data generating process, we resample the data in blocks, with block sizes of 4; 5; 6; 8; 10, and

12 observations for the cases n 1; 2; 3; 4; 5; 6, respectively. The bootstrap p-value is computed as the percentage of synthetically generated t-statistics

that exceed the actual t-statistic in absolute value.7 The unannualized excess return on the six-month-ahead contract is, on average, $5 million times 0.307% times 112. The annualized excess return is

just double this amount (multiplying by 126 ). Bidask spreads on fed funds futures contracts are typically small, usually around 1 bp even for long-maturity

contracts. On days of very high volatility, spreads for long-maturity contracts (n 5; 6 months) can reach 20 bp, but these spikes are very short-lived and

can easily be avoided by trading just one or two days later. All of our findings of excess returns are thus robust to the presence of bidask spreads on thesecontracts.



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The averages for the post-1994 period are a little lower but still significantly positive at 24.9, 27.2, 29.0, 32.7, 37.0, and

42.9 bp per year.

2.2. Excess returns and recessions

Under the expectations hypothesis, excess returns on bonds and interest-rate futures are assumed to be constant over

time. However, there is by now a large body of literature that finds excess returns on Treasury securities to be significantly

time-varying and predictable (e.g., Fama and Bliss, 1987; Campbell and Shiller, 1991; Cochrane and Piazzesi, 2005). Fig. 1

plots the realized excess return on the four-month-ahead federal funds futures contract, rx4t4 , from October 1988 through

December 2005, with each point in the graph depicting the realized excess return, f4t rt4, at date t. Certainly, the time

variation in this realized excess return series has been large, ranging from 315 to 413 bp at an annualized rate. The graph

also suggests that there have been several periods during which fed funds futures generated particularly large excess

returns: the years 19911992, early 1995, the fall of 1998, and the years 20012002 (these are also the periods during

which the Federal Reserve lowered interest rates). Two of these periods, 19911992 and 20012002, coincided with the

two recessions in our sample. The other two periods were not recessions, but were also periods with slower economic

growth.

Panel B in Table 1 reports the results from regressing the excess returns on fed funds futures on a constant and a

recession dummy Dt:

rxntn an bnDt

ntn. (3)

The recession dummy is significant for all contracts with maturities longer than just one month. The estimated

coefficient on the recession dummy suggests that expected excess returns are countercyclical; expected excess

returns are about 35 times higher in recessions than they are on average during other periods. (Note that

annualizing the excess returns is a normalization that does not affect the t-statistics or R2 in any of our

regressions.) The fitted values from regression (3) for the four-month-ahead contract are depicted by the gray line

in Fig. 1.

Of course, recession dummies are not useful as predictive variables in real time, since the NBERs business-cycle dating

committee declares recession peaks and troughs as long as two years after they have actually occurred. Fig. 1 suggests,

however, that any macroeconomic or financial business-cycle indicator may be a good candidate for forecasting excess

returns on fed funds futures contracts, an exercise to which we now turn.

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

400

300

200

100

0

100

200

300

400

500

basis

points

Fig. 1. Annualized excess returns on the federal funds futures contract four months ahead. The gray step function represents the fitted values from aregression of rx4t4 on a constant and a recession dummy.



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2.3. Employment growth as a predictor of excess returns

To investigate whether a variable or set of variables forecasts excess returns on federal funds futures, we run predictive

regressions of the form:

rxntn an bnXt

ntn, (4)

whereXt is a vector of variables known to financial markets in month t. Since GDP is only available at quarterly frequency, itis not a useful variable for forecasting monthly excess returns. We therefore turn to a closely related indicator of real

activity: employment. More precisely, we use the year-on-year change in the logarithm of U.S. nonfarm payroll

employment, being careful to use data that were available to financial market participants in real time (that is, as of the last

day of month t).8

Panel C ofTable 1 reports the forecasting results from regression equation (4) based on these real-time nonfarm payroll

numbers. The regression also includes the futures rate itself on the right-hand side, as is common practice. The results

show that employment growth is a significant predictor of excess returns for contracts with two months or more to

maturity. Fitted values from regression (4) for the four-month-ahead contract are depicted by the gray line in Fig. 2. As we

would expect from our results using the recession dummy, expected excess returns are countercyclical in Fig. 2: expected

excess returns and employment growth are inversely related. The estimated slope coefficients in Panel C increase with the

maturity of the contract and lie between 0:20 and 0:73 for annualized returns.

To understand the magnitude of these coefficients, note that employment growth is measured in basis points, which

means that a 1 percentage point drop in employment growth increases expected excess returns on federal funds futures byabout 2073bp per year. Over our sample, the mean and standard deviation of employment growth were 135 and 132 bp,

respectively, which means that a one-standard deviation shock to employment makes us expect around 95 bp more in

annualized excess returns on the six-month-ahead futures contract. The own futures contract rate fnt is also a significant

predictor of excess returns for these contracts, and the positive coefficient implies that, all else equal, excess returns are

lower when the level of interest rates is lower.9

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

400

300

200

100

0

100

200

300

400

500

basis

points

Fig. 2. Annualized excess returns on the federal funds futures contract four months ahead. The gray function represents the fitted values from a regression

of rx4t4 on a constant, employment growth and f4t itself.

8 Two data issues arise if we wish to run the predictive regressions (4) with data that were available to financial market participants in real time. First,

nonfarm payroll numbers for a given month are not released by the Bureau of Labor Statistics until the first Friday of the following month. Thus, to

perform the predictive regressions (4) with data that were available at the end of month t, we must lag the employment numbers by an entire month.

Second, nonfarm payroll numbers are revised twice after their initial release and undergo an annual benchmark revision every June, so the final vintage

numbers are not available for forecasting in real time. We therefore collected the real-time nonfarm payroll numbers, and use the first release of nonfarm

payrolls for month t 1 and the revised value for nonfarm payrolls for month t 13 to compute the year-on-year change. Even the revised value for

month t 13 is not quite equal to the final vintage of data for that month, because the BLS performs occasional benchmark revisions.

9 As a robustness check, we re-ran the predictability regressions in Table 1 using the current-month fed funds rate rt instead of the own futurescontract rate f

nt . The results (not reported) are similar to those based on the futures rate. For example, the R

2 are identical to those in Panel C. We also ran



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The R2 in Panel C suggest that we can predict up to 39% of the variation in excess returns on federal funds futures with

employment growth and the futures rate itself. This result is remarkable, since these R2 are comparable in size to those

reported in Cochrane and Piazzesi (2005), who study excess returns on Treasuries over much longer holding periods (one

year, as compared to just one to six months for our fed funds futures regressions above).

2.4. Financial market variables as predictors of excess returns

We can also try to forecast excess returns on fed funds futures using financial indicators of the business cycle, whichhave the advantage of being available at higher frequencies than macroeconomic indicators. Panel D in Table 1 reports the

results for one such indicator, the spread between BBB-rated 10-year corporate bonds and the 10-year Treasury yield.

(In the NBER working version of this paper, we report similar results for Treasury yield spreads, another widely used

financial indicator.) The results lend additional support to the hypothesis that business-cycle indicators are useful

predictors of excess returns in the fed funds futures market. The estimated coefficients on the corporate bond spread in

these regressions are significant for fed funds futures contracts with two months or more to maturity, with R2 that range

from 8% to 22%. Although we do not graph the corporate bond spread here in the interest of space, it is most successful at

capturing the runups in excess returns in 19901993 and 20012002, further suggesting that the predictive power of these

financial indicators may be largely due to the relationship between excess returns and the business cycle.

By contrast, a time-varying measure of the risk premium proposed by Sack (2004), which is based on the slope of the

eurodollar futures curve from four to five years ahead and is not closely tied to the business cycle, performs poorly at

forecasting excess returns in the futures markets. Sacks long-horizon eurodollar slope is never statistically significant for

any of our fed funds future contracts (t-statistics never exceed 0.7 in absolute value), with R2 below 5%.10 Moreover, thecoefficient estimates on this slope have the wrong sign: Sacks analysis suggests that they should be positivea high

slope represents a higher risk premium and higher excess returnbut in fact our coefficient estimates find that this

relationship is negative.

3. Robustness and real-time predictability of excess returns

Our results above provide substantial evidence for time variation of risk premia in federal funds futures. We now

perform a variety of robustness checks and sensitivity analysis of this basic result.11 We devote particular attention to

assessing whether these excess returns were predictable in real time, looking at rolling-endpoint regressions and also some

intriguing historical evidence on the actual positions taken by non-hedging traders in the federal funds futures and

eurodollar futures markets.

3.1. One-month holding period excess returns

Our sample period spans only about 17 years, which results in as few as 34 independent windows for our longest-

horizon (six-month-ahead) fed funds futures contracts. A way to increase the number of independent observations in our

regressions and check the robustness of our results is to consider the excess returns an investor would realize from holding

an n-month-ahead fed funds futures contract for just one monthby purchasing the contract and then selling it back as an

n 1-month-ahead contract in one months timerather than holding the contract all the way through to maturity. By

considering one-month holding period returns on fed funds futures, we reduce potential problems of serial correlation and

sample size for the longer-horizon contracts, and give ourselves 206 independent windows of data (under the null

hypothesis of no predictability of excess returns) for all contracts.

We thus consider regressions of the form

fn

t f

n1

t1 an bnX

t n

t1, (5)

where fnt denotes the n-month-ahead contract rate on the last day of month t, f

n1t1 denotes the n 1-month-ahead

contract rate on the last day of month t 1, and the difference between these two rates is the ex post realized one-month

holding period return on the n-month-ahead contract. Using specification (5), the residuals are serially uncorrelated under


predictability regressions including both rt and fnt . The results (also not reported) did not significantly improve upon those in Panel C, except for the one-

month-ahead contract. For n 1; we obtain significant slope coefficients for all RHS variables with an R2 of 5%. The estimated slope coefficients on fnt and

rt almost offset each other, the former being somewhat bigger. We also ran regressions with the most recent revised vintage of the employment data, and

our results are similar: in particular, we find that employment growth predicted excess returns with R2 values of 1%; 7%; 14%; 20%; 28%, and 37%. The

results are also similar if we use contemporaneous rather than lagged nonfarm payrolls growth as a regressor.10 The estimated coefficients on Sacks long-horizon eurodollar slope are 0 :94; 0:51; 3:42; 11:3; 17:5, and 19:3 at the n 1; 2; 3; 4; 5; 6 horizons,

with t-statistics of 0:1; 0:0; 0:2; 0:5; 0:7, and 0:7, respectively.11 In Piazzesi and Swanson (2006), we also extended the results of Section 2 to eurodollar futures, which have traded on the Chicago Mercantile

Exchange since 1981 and have quarterly expirations which settle based on the spot eurodollar (LIBOR) rate in effect at expiration. Our findings foreurodollar futures contracts were very much in line with those for fed funds futures above.



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the null hypothesis of no predictability of excess returns, because all variables in Eq. (5) are in financial markets

information set by the start of the next period.

Table 2 presents the results of our previous analysis applied to this alternative specification, where the regressors arethe own contract rate and employment growth. Although the R2 values are uniformly lower, as is to be expected from

quasi-first-differencing the left-hand side variable, our previous results are robust to this alternative specification. Results

for term spreads and corporate bond spreads are similarly robust across specifications. (These results are not presented to

conserve space.)

3.2. Rolling-endpoint regressions

We have documented that excess returns on fed funds futures were predictable using business-cycle indicators such as

employment growth, corporate bond spreads, and Treasury yield spreads. To what extent could an investor have predicted

these returns in real time, using only data that was available up to that point in time? To answer this question, we perform

a set of rolling-endpoint regressions.

Fig. 3 shows real-time forecasts of excess returns on the four-month-ahead fed funds futures contract togetherwith the full-sample forecasts from Panel C in Table 1 based on employment growth and the own futures contract rate.

Table 2

One-month holding period excess returns and nonfarm payrolls

n 1 2 3 4 5 6

Constant 0.3 6.3 5.8 5.4 14.2 69.1

(t-Stat) (0.0) (0.2) (0.2) (0.1) (0.3) (1.2)

fnt

0.13 0.23 0.34 0.41 0.47 0.69

(t-Stat) (2.4) (3.1) (3.7) (3.8) (3.8) (4.7)

DNFPt1 0.19 0.55 0.76 0.92 1.02 1.15

(t-Stat) (2.0) (4.1) (4.8) (5.0) (4.9) (5.0)

R2 0.03 0.08 0.10 0.11 0.11 0.14

Note: n denotes the horizon of the fed funds futures contract in months. The sample for each regression is 1988:102005:12 at monthly frequency,

sampled on the last day of each month. Excess returns are measured in annualized basis points (i.e., one-month excess returns are multiplied by 12). HAC

t-statistics are reported in parentheses. The regression equation is (5), where Xt contains fnt and nonfarm payroll employment growth DNFPt1 from

t 13 to t 1. DNFPt1 is measured in basis points.

1992 1994 1996 1998 2000 2002 2004 2006

500

0

500realtime forecast

fullsample forecast

1992 1994 1996 1998 2000 2002 2004 2006

1

0

1

2

3

4

own futures rate cofficient

1992 1994 1996 1998 2000 2002 2004 2006

4

3

2

1

0

NFP coefficient

Fig. 3. The top panel shows real-time and full-sample forecasts of rx4t4. The middle panel shows the gray rolling estimates of the coefficient on the own

futures rate f4t . The flat black line is the full-sample coefficient from Table 1. The lower panel shows the gray rolling estimates of the coefficient on

employment growth. Again, the flat black line is the full-sample coefficient from Table 1.



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The real-time forecasts for each month t are constructed by estimating the slope coefficients with data from October 1988

up through what was available at the end of the previous month t 1. Fig. 3 graphs these forecasts starting in October

1990, when we have only 24 months of data to estimate the three parameters of the model. The graph suggests that the

real-time fitted values are quite close to the full-sample fitted values over most of the sampleindeed, the two series are

essentially identical from the beginning of 1994 onward. The middle and lower panels in Fig. 3 show the rolling estimates

of the slope coefficients together with their full-sample counterparts (the horizontal black line), and again suggest that the

rolling point estimates have largely converged to their full-sample values by 1994.

3.3. Data on non-hedging market participants positions

The previous section shows that excess returns on fed funds futures were potentially predictable to investors in real

time using rolling regressions. In this section, we present some evidence indicating that informed investors at the time

actually did correctly forecast the excess returns that were subsequently realized.

The U.S. CFTC requires all individuals or institutions with positions above a certain size to report their positions to the

CFTC each week, and the extent to which each position is hedged. In the eurodollar (federal funds) futures markets, about

90% (95%) of open interest is held by individuals or institutions that must report to the CFTC as a result of this requirement.

The CFTC reports the aggregates of these data with a three-day lag, broken down into hedging and non-hedging categories

and into long and short positions, in the weekly Commitments of Traders report, available online.

The lower panel in Fig. 4 plots the percentage of long and short open interest in eurodollar futures held by

noncommercial market participantsthose market participants that are classified by the CFTC as not hedging offsetting

positions that arise out of their normal (non-futures related) business operations.12 The number of open long positions in

these contracts held by noncommercial market participants (as a percentage of total reportable open interest) is depicted

in the bottom panel of the figure by the black line, and the number of open short positions (as a percentage of reportable

open interest) by the gray line.13 The upper panel ofFig. 4 plots the difference between the noncommercial percentage long

and short series as the net long position of noncommercial market participants.

The net long position graphed in Fig. 4 displays a clear positive correlation with the excess returns in federal funds

futures contracts depicted in previous figures: for example, noncommercial market participants began taking on a huge net

long position in late 2000, just a few months before excess returns in these contracts began to soar, and they took on

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

20

10

0

10

20

30

percent

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

0

10

20

30

40

percent

Fig. 4. The upper panel shows net positions in eurodollar futures. The lower panel shows long (black) and short (gray) positions separately.

12 The primary example of a commercial participant in the federal funds or eurodollar futures market would be a financial institution seeking to hedge

its commercial and industrial loan portfolio. For more details on the institutional features of these markets, see Stigum (1990).13 Analogous data are available for fed funds futures positions as well, but we focus on eurodollar futures positions here as this market is thicker and

contracts run off less frequentlyonly once per quarter rather than every monthwhich reduces some high-frequency variation in the percentage long

and short series. Open interest is almost always highest in the front-month or front-quarter contract, so the running off of these contracts can create

jumps. The patterns in fed funds futures noncommercial market participant holdings are similar to those in eurodollar futures, albeit noisier for thisreason.



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substantial long positions in mid-1990 through mid-1991 and late 1995 as well, again correctly forecasting excess returns

over these periods; noncommercial market participants also took on a very substantial short position in late 1993 through

mid-1994, correctly anticipating the low or even negative excess returns that were subsequently realized when the Federal

Reserve began tightening policy in 1994.

These casual observations are confirmed in regression results (reported in Piazzesi and Swanson, 2006). The net long

position variable is a significant predictor of excess returns in the fed funds futures market at horizons of two months or

more, with R2 values from 5% to 25%. Interestingly, the statistical significance of the net long position variable disappears if

we also include any of employment growth, term spreads, or corporate risk spreads in the regression, suggesting that theinformation content of noncommercial market participants net position is spanned by the business-cycle indicators that

we have already considered in Section 2.

These results suggest that noncommercial market participants were aware of the upcoming excess returns in the market

and positioned themselves accordingly, at the expense of those engaged in hedging other financial activities. The

hedgersprimarily banksessentially paid an insurance premium to noncommercial participants for providing hedging

services. There are two primary explanations for why these premia were not competed away by the market. First, the

futures market may not be perfectly competitive, with barriers to entry and noncommercial market participants facing

limits on the size of the positions that they may take; commercial participants with hedging demand thus may not face a

perfectly elastic supply curve for either the long or short side of these futures contracts. Second, noncommercial market

participants may themselves be risk averse; for example, futures traders in these markets may be most averse to taking on

large bets or risky positions precisely when their own jobs are most in jeopardy, around the times of recessions. The

hypothesis that excess returns in these markets would be competed away requires both an assumption of perfectly

competitive futures markets and of risk-neutral market participants, and both of these assumptions may not apply.

4. Risk-adjusted measures of monetary policy expectations

How misleading would it be to ignore risk premia on federal funds and eurodollar futures and treat the unadjusted

prices of these securities as measures of monetary policy expectations? Using futures, the forecast errors are just minus the

excess returns on the fed funds futures contract:

rtn fnt rx

ntn. (6)

To the extent that excess returns on federal funds and eurodollar futures are forecastable, one would be making systematic

forecast errors if one used unadjusted futures rates as measures of monetary policy expectations.

However, we can risk-adjust these futures rates using our previous results. To do that, we take expectations of both sides

of Eq. (4) and solve for the expected n-month-ahead federal funds rate:

Etrtn fnt a

n bnXt. (7)

From Table 1, we know that the expected excess return, an bnXt, is on average positive. This suggests that risk-adjusted

forecasts lie on average below the futures rate. Moreover, Table 1 shows that expected excess returns are countercyclical.

This suggests that risk-adjusted forecasts subtract a countercyclical term from the futures rate or, equivalently, add a

procyclical term to the futures rate: risk-adjusted forecasts will tend to lie above the unadjusted futures rate in booms and

below the futures rate in recessions.

These features of our risk-adjustment are illustrated in Fig. 5, which plots forecasts of the federal funds rate out to a

horizon of 12 months on two different dates: December 1993 and December 2000. We plot a number of alternative

forecasts based on federal funds and eurodollar futures rates:

1. Unadjusted futures: an 0 and bn 0.

2. Rule-of-thumb-adjusted futures: a constant risk adjustment of 1 bp per month, which is a rule of thumb that has been

used by staff at the Federal Reserve Board for these interest-rate futures,14 so an n and bn 0. For eurodollar futures,

the rule of thumb is 13bp plus 3 bp per quarter: an 3n 13 and bn 0.

3. Risk-adjusted futures: rolling OLS estimates ofan and bn, where Xt includes the own futures rate fnt and NFP growth

DNFPt1, as in Panel C of Table 1 for fed funds futures and eurodollar futures.

Fig. 5 illustrates that unadjusted futures forecasts are always higher than rule-of-thumb-adjusted forecasts. The two

panels in Fig. 5 suggest that in times when the funds rate is expected to risesuch as December 1993the higher,

unadjusted futures therefore do better than rule-of-thumb-adjusted futures. However, the lower, rule-of-thumb-adjusted

futures do better in times when the funds rate is expected to fall, such as December 2000. This is exactly the mechanism

14 In private communication dated May 2004, Donald Kohn mentioned that staff at the Federal Reserve Board came up with this adjustment factor

informed by their reading of the historical data on ex post errors in the federal funds and eurodollar futures markets and in interest-rate surveys. Although

this adjustment factor was 1 bp per month at the short end of the futures curve at the time of that communication, he noted it has not always been thatand would change as events warrant.



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exploited by our time-varying risk adjustment: in December 1993, our risk-adjusted futures forecast (the x-line) is closer to

the unadjusted futures forecast, while in December 2000, the x-line is closer to the rule-of-thumb-adjusted futures

forecast.Fig. 5 suggests that unadjusted futures rates, or futures adjusted by a constant, can be wrong over long periods of time.

The forecast errors tend to be negative during periods of falling rates and positive during periods of rate hikes. The forecast

errors are largest when the funds rate changes direction, and keep being large for substantial amounts of time. The reason

is that unadjusted or constant-adjusted futures rates only slowly adapt to changes in direction. As a result, these forecasts

tend to lag behind actual market expectations around economic turning points; they generate forecast errors that are more

autocorrelated than forecast errors from risk-adjusted futures.

To see this point more clearly, Table 3 reports some summary statistics for forecast errors, for each of a number of

different forecasts. We compute forecast errors from futures-based forecasts and also from a simple vector autoregression

(VAR) as a benchmark.15 The VAR is computed at monthly frequency using four lags of each of the fed funds rate, the year-

on-year percentage change in the core CPI, and the year-on-year percentage change in nonfarm payroll employment.16 We

compute forecasts for the n-month-ahead fed funds rate as it would have been made at each time t, using real-time data

and rolling-endpoint regressions. For example, when we compute forecasts for rtn using the VAR benchmark, we estimate

the parameters of the VAR using only data up through time t 1 and then use the values of the fed funds rate, core CPIinflation, and nonfarm payrolls growth at time tas the conditioning variables for the forecast. Similarly, we use our rolling

out-of-sample forecasts for risk premia based on nonfarm payrolls growth to make our risk adjustments. The forecast

errors are computed over the October 1990December 2005 period, so that we have two years of data to estimate the

parameters for the October 1990 forecast.

Table 3 reports mean forecast errors (ME), root-mean-squared errors (RMSE), and the nth autocorrelation (rn) for the

n-month-ahead forecast. (Note that even for an efficient n-month-ahead forecasts, the forecast errors would have an

MAn 1 autocorrelation because of forecast overlap; Table 3 therefore reports the nth autocorrelation which, ideally,

should be zero.) The last column of Table 3 shows that risk-adjusted futures still made autocorrelated forecast errors over

0 2 4 6 8 10 12

3

3.5

4

4.5

5

percent

Expected Fed Funds Rate Derived From Futures Rates on Dec 1993

0 2 4 6 8 10 12

2

3

4

5

6

months ahead

percent

Expected Fed Funds Rate Derived From Futures Rates on Dec 2000

unadjustedruleofthumbadjustedriskadjustedex post realized

Fig. 5. Federal funds rate forecasts on two illustrative dates, and subsequent realized funds rate. Funds rate forecasts are constructed from unadjusted and

risk-adjusted futures rates, and using three different risk adjustments: an estimated constant adjustment, a rule-of-thumb-constant adjustment, and a

time-varying risk adjustment based on employment growth.

15 We also considered forecasts from an AR(1) and a random walk. The resulting forecasts, however, were outperformed by the VAR, so we did not

include them in Table 3 to conserve space. Another alterative are Taylor-rule forecasts. For forecasts up to three months ahead, Evans (1998) documents

that they tend to be dominated by forecasts based on (unadjusted) futures.

16 The lag length was selected to yield good empirical forecast performance: more lags than 4 tended to lead to overfitting and poor forecastperformance, while fewer lags tended to lead to overly simple dynamics and poor forecast performance.



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our sample, but the autocorrelation is much smaller than for any other forecast in the table. This is especially true for

longer forecasting horizons. Moreover, risk-adjusted futures generate smaller average errors and lower root-mean-square

errors.

Interestingly, Panel A makes a strong case for fed funds futures in general, even on a risk-unadjusted basis. The futures-

based forecasts produce lower root-mean-square errors than a VAR. However, unadjusted futures made large, negative

errors on average, ranging from 3 to 31bp. The rule-of-thumb-adjusted futures improve upon this: average forecast errors

are lower by exactly the amount of the adjustment, and the adjustment also lowers mean-square errors. However, this

adjustment only represents a small improvement over unadjusted forecasts. The risk-adjusted forecasts we estimate in this

paper generate forecast errors that are always smaller on average and almost always smaller in root-mean-square terms,

especially for longer forecasting horizons. Panel B confirms these findings for longer-horizon forecasts using eurodollar

futures.17 Again, risk-adjusted futures do much better than unadjusted futures or the rule-of-thumb-adjusted futures.

5. Monetary policy shocks

Fed funds futures have also been used by a number of recent authors to separate systematic changes in monetary policy

from monetary policy shocks.18 The idea is to use fed funds futures market forecast errors as measures of exogenous,

unforecastable changes in the stance of monetary policy.19 The fed funds futures market expectation is measured assuming

the expectations hypothesis. Since we have shown in the previous section that futures rates should be adjusted for time-

Table 3

Forecasts of the federal funds rate

Benchmark Federal funds futures-based forecasts

VAR(4) Unadjusted future Rule-of-thumb-adjusted futures Risk-adjusted futures

n ME RMSE rn ME RMSE rn ME RMSE rn ME RMSE rn

(A) Federal funds rate forecasts1 1.4 27 0.67 3.2 11 0.10 2.2 11 0.06 0.5 12 0.08

2 1.1 36 0.57 7.6 19 0.28 5.6 18 0.23 2.1 19 0.19

3 1.9 47 0.39 12.4 29 0.37 9.4 28 0.33 4.3 29 0.20

4 2.6 57 0.24 18.2 41 0.39 14.2 40 0.34 7.0 38 0.16

5 3.6 66 0.13 24.7 54 0.40 19.8 52 0.40 8.7 46 0.14

6 5.2 75 0.08 30.8 66 0.49 24.8 64 0.45 8.9 50 0.16

Benchmark Eurodollar futures-based forecasts

VAR(3) Unadjusted future Rule-of-thumb-adjusted futures Risk-adjusted futures

n ME RMSE rn ME RMSE rn ME RMSE rn ME RMSE rn

(B) Eurodollar rate forecasts

1 15 120 0.80 17 44 0.40 1 40 0.29 7 38 0.072 27 135 0.45 43 89 0.56 24 81 0.48 21 64 0.28

3 31 144 0.10 73 134 0.57 51 123 0.51 37 90 0.17

4 25 161 0.22 105 182 0.47 80 169 0.39 54 116 0.04

5 11 180 0.34 135 223 0.38 107 207 0.30 68 138 0.05

6 17 198 0.26 163 256 0.31 132 238 0.22 83 159 0.16

7 45 209 0.13 181 281 0.26 147 260 0.16 86 179 0.16

8 72 206 0.17 200 297 0.25 163 274 0.15 92 195 0.06

Note: n is the forecasting horizon in months (quarters for eurodollar rate). ME denotes the mean forecast error (in basis points), RMSE the root-mean-

squared error (in bp), and rn is the nth autocorrelation of the forecast error, all over the period 1990:102005:12 (1990Q32005Q4 for eurodollars).

VAR(4) is a monthly VAR forecast based on four lags of each of the federal funds rate, year-on-year percentage change in the core CPI, and year-on-year

percentage change in nonfarm payrolls. VAR(3) is a quarterly VAR based on three quarterly lags of the 90-day eurodollar rate, year-on-year percentage

change in the core CPI, and year-on-year percentage change in nonfarm payrolls. The risk-adjusted futures-based forecast adjusts the fed funds futures

rate for risk premia using the own futures rate and the year-on-year percentage change in nonfarm payrolls. Coefficients of the VAR and the risk-

adjustment regression are recomputed at each date t using data only up through month t 1, so all forecasts are pseudo-out-of-sample.

17 The VAR for the 90-day eurodollar rate uses the same variables as the monthly VAR but sampled at quarterly frequency beginning in 1990Q3 with

data going back to 1985Q1. We chose a lag length of 3 since this seemed to give good empirical forecast performance: a lag length of 4 performed worse

and a lag length of 2 performed better at the shortest horizons but worse at longer horizons.18 See, e.g., Rudebusch (1998), Cochrane and Piazzesi (2002), and Faust et al. (2004) for different approaches. All of these studies treat the federal

funds rate as the monetary policy instrument, as in Bernanke and Blinder (1992), and attempt to improve upon the earlier VAR-based identification of

monetary policy shocks surveyed in Christiano et al. (1999).

19 Faust et al. (2004) describe the procedure in detail and test many of the required assumptions. Alternatively, Piazzesi (2005) and Cochrane andPiazzesi (2002) measure market expectations from high-frequency data on short-term interest rates instead of fed funds futures. Piazzesi (2005)



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varying risk premia, we now investigate to what extent these risk premia might affect futures-based measures of monetary

policy shocks.

Computing the futures markets forecast error of the next policy move is less straightforward than it may seem, because

of some institutional features of the fed funds and fed funds futures markets. For example, the futures contract settles

based on the average fed funds rate that is realized during the contract month, and not on the value of the funds rate on a

particular date, such as the day following an FOMC meeting. Moreover, the Federal Reserve sets a target for the funds rate,

but does not completely control the funds rate itself, and the difference between the actual funds rate and the target can be

nonnegligible, even for monthly averages. In the literature, these complications have led to alternative approaches on how

policy shocks are computed from futures rates.

Here, we consider the two primary approaches to measuring monetary policy shocks that have been used in the

literature. First, Rudebusch (1998) suggests defining the monetary policy shock as the difference between the realized fed

funds rate target and the expected fed funds rate derived from fed funds futures. While this might seem to be the most

natural definition of the markets forecast error, it can suffer from the technical issues described above that cause the

market expectation of the future realized funds rate to differ from the market expectation of the future target rate. More

importantly, monetary policy shocks measured in this way will be contaminated by risk premia in the futures market even

if those risk premia are constant. Our second measure of monetary policy shocks, suggested by Kuttner (2001), differencesout both the technical factors in the fed funds market and any constant risk premia by using the change in the current-

month or one-month-ahead fed funds futures rate on the day of an FOMC announcement. This approach uses daily fed

funds futures data to make the interval t; t 1 around the FOMC announcement small and assumes that risk premia do

not change over this small interval.20

We compute these two measures of monetary policy shocks over the sample period 19942005, when the Federal

Reserve was explicitly announcing changes in its target for the fed funds rate. We include every FOMC meeting and every

intermeeting policy move by the FOMC over this sample. Table 4 reports summary statistics for both measures of policy

shocks. From Panel A it is apparent that the first measure of monetary policy shocks, labeled actual-futures, is larger and

more volatile than the second measure: the mean, standard deviation, and extremes of the shocks are all larger in the first

shock series than in the second. The two shocks series do generally agree on the days of large monetary policy shocks,

howeverfor example, the min and max of the two series both occur on the same days.

We investigate the robustness of the two monetary policy shock series to risk premia by regressing them on a set of

conditioning variables that were known to financial markets right before the FOMC announcement

for this exercise, wepick Treasury yields as the regressors, because we have high-frequency data on these yields.21 Under the expectations

hypothesis, each monetary policy shock measure should be unpredictable on the basis of these conditioning variables.

Results for these regressions are summarized in Panel B of Table 4, which also reports the p-values from a zero-slopes

F-test that all of the coefficients (excluding the constant term) in each regression are jointly equal to zero. As can be seen in

Table 4

Risk-adjusting measures of monetary policy shocks

Actual-futures Change in FF futures

Original Adjustment Original Adjustment

Panel A: summary statistics of policy shocks

Mean 3.0 3.0 1.2 1.2

Std. dev. 11.0 3.2 8.2 2.0Min 43.8 12.6 42.5 6.4

Max 17.1 4.1 14.5 15.2

Constant 1 year6 months 21 years 52 years 105 years R2 p-value

Panel B: t-statistics from regressions on Treasury spreads

Actual-futures 2.0 1.7 2.6 2.5 2.2 0.09 0.054

Change in FF futures 1.5 0.6 1.8 1.6 1.3 0.06 0.431

Note: Daily observations on days of FOMC meetings and intermeeting policy moves, 19942005.


computes Etrt1 from an arbitrage-free model of the term structure of interest rates. Cochrane and Piazzesi (2002) use the change in the one-month

eurodollar rate and unrestricted regressions of rt1 on a set of interest rates.20 This assumption is consistent with the finding by Evans and Marshall (1998) that risk premia in Treasuries show only a small response to monetary

policy shocks in a VAR. It is also potentially consistent with our findings above and those of Cochrane and Piazzesi (2005) that risk premia vary

substantially at business-cycle frequencies but perhaps do not vary as much at higher frequencies.21 Results using corporate bond spreads are very similar. In both cases, we reestimate the predictability regression coefficients for the monetary policy

shock series for two reasons: first, risk premia depend on the maturity of the contract and FOMC meetings are typically not scheduled for the end of the

month, and second, the risks associated with monetary policy shocks (and therefore the risk premia associated with these shocks) may have changed after1994, when the Fed started announcing its policy moves at FOMC meetings, as argued in Piazzesi (2005).



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the table, our first measure of monetary policy shocks (the realized target rate minus the futures market expectation)

appears to be significantly contaminated both by a constant risk premium (as evidenced by the t-statistic for the constant

term) and possibly also by time variation in risk premia (as evidenced by the zero-slopes F-test, which is borderline

statistically significant). In contrast, our second policy shock measure (the one-day change in the federal funds futures rate)

seems to do much better: no coefficient is statistically significant, and we do not reject the null of no contamination by

time-varying risk premia.

Panel A of Table 4 also reports basic statistics for our estimated risk adjustments to each of the three monetary policy

shock series. The risk adjustments for our first shock measure (actual-futures) has a standard deviation of 3.2 bp, whichseems substantial relative to the standard deviation of the shock series itself of 11 bp. In contrast, the estimated risk

adjustments to our second measure of monetary policy shocks are much smaller as well as statistically insignificant.

We infer from this analysis that monetary policy shocks based on the difference between the realized federal funds rate

target and the unadjusted federal funds futures-based forecast, as suggested by Rudebusch (1998), are significantly

contaminated by risk premia, both on average and by an amount that varies over time. The primary alternativemeasuring

monetary policy shocks based on the one-day change in the federal funds futures rate around FOMC announcements, as

suggested by Kuttner (2001)seems to be much more robust to the presence of risk premia in these contracts. The

difference-based measure may largely difference out risk premia that are moving primarily at lower, business-cycle

frequencies, consistent with our analysis in Section 2 and the findings in Cochrane and Piazzesi (2005).

6. Conclusions

We document substantial and predictable time variation in excess returns on federal funds futures. We show that excessreturns on these contracts are strongly countercyclical and can be predicted with R2 of up to 39% using contemporaneous

macroeconomic and financial business-cycle indicators such as employment growth, Treasury yield spreads, and corporate

bond spreads. We also present evidence that suggests that market participants could have been and in fact were aware of

these excess returns in real time, as evidence by real-time rolling-endpoint regressions and the observation that non-

hedging futures market participants were large buyers of these contracts in times of high expected excess returns and large

sellers in times of low or negative expected excess returns.

Our findings of predictable excess returns in federal funds futures contracts have important consequences for

computing market expectations from these futures rates. We find that ignoring these risk premia substantially increases

forecast errors, both on average and in terms of root-mean-squared error. Moreover, unadjusted futures make forecast

errors that are more autocorrelated, because unadjusted futures-based forecasts lag behind our risk-adjusted forecasts

around economic turning points. Finally, we show that measures of monetary policy shocks based on the realized funds

rate target minus the ex ante unadjusted fed funds futures rate are significantly contaminated by risk premia. Instead, a

measure of monetary policy shocks based on the one-day change in federal funds futures around FOMC announcementsseems to be more robustfor instance, it may largely difference out risk premia that move primarily at lower, business-

cycle frequencies.

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